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Physica C 453 (2007) 12­14 www.elsevier.com/locate/physc

Superconducting temperature of the x-phase in Ti, Zr and Hf metals at high pressures
I.O. Bashkin *, V.G. Tissen, M.V. Nefedova, E.G. Ponyatovsky
Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russia Received 27 November 2006; accepted 29 November 2006 Available online 24 January 2007

Abstract The superconducting transition temperature of the Ti metal is measured in dependence on pressure to 56.0 GPa. A linear Tc(P) increase is observed in the stability range of x-Ti, like in the Zr and Hf x-phases. This general behavior can be related to low electron density of states at the Fermi level at zero pressure and its pressure-induced increase due to the s­d electron transfer. ñ 2006 Elsevier B.V. All rights reserved.
PACS: 74.62.Fj Keywords: Superconducting transition temperature; High pressure; Titanium; Zirconium; Hafnium

At normal conditions Ti, Zr and Hf are stable in the hexagonal close-packed structure (the hcp a-phase). These three a-phases at atmospheric pressure are low-temperature superconductors with the Tc values in the range 0.25­0.50 K for a-Ti (depending on the sample pre-history), 0.45­1.1 K for a-Zr and 0.128 K for a-Hf [1­3]. Applied pressure induces a transition from the a-phase to the hexagonal x-phase [1]. The a­x transition is reversible in Hf [4], but does not occur in Ti and Zr on decompression at room temperature so that x-Ti and x-Zr remain intact at ambient conditions infinitely. At normal pressure x-Zr is a superconductor, Tc = 0.65 K [2] to 0.95 K [3], but superconductivity was not observed in x-Ti at P = 1 atm down to T = 0.06 K [3]. The pressure effect on the superconducting temperature of x-Zr was studied in several works [5­ 7], and Tc was found to increase until the x­b transition in Zr. A similar Tc(P) dependence was recently observed on Hf [8].

*

Corresponding author. Fax: +7 96 5249701. E-mail address: bashkin@issp.ac.ru (I.O. Bashkin).

In this work we measured the superconducting transition temperatures of titanium up to P = 56 GPa and found that the x-phases of all three metals are superconductors under high pressure. The Ti metal studied was prepared from a rod of iodiderefined Ti by means of the electron-arc zone melting in vacuum. The total impurity contents was less than 0.02 at.%. The sample was cut from a Ti chip polished to less than 0.02 mm thick. High pressure was generated using the diamond-anvil apparatus made of non-magnetic materials [8]. The pressure-transmitting medium was the 4:1 methanol­ethanol mixture. The superconducting transitions were recorded as anomalies in the temperature dependence of the magnetic susceptibility, v(T), measured with the alternating current of a 5.2 kHz frequency on heating the sample from the minimum temperature. The minimum temperature of about 1.3 K was obtained by vacuum pumping of the He cryostat with the high-pressure apparatus inside. The (Cu­Fe)­Cu thermocouple was used for the temperature measurements with an accuracy of ±0.2 K. Pressure was determined from the shift of the ruby luminescence line [9] after recovery of the press to room temperature at the

0921-4534/$ - see front matter ñ 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2006.11.014


I.O. Bashkin et al. / Physica C 453 (2007) 12­14

13

-Ti

Tc
40.9 45.2 51.0 56.0 GPa

1.5

2.0

2.5

3.0

3.5

4.0

T (K)
Fig. 1. Magnetic susceptibility curves, v(T), measured on Ti at the indicated pressure values. The geometric scheme illustrates the graphical determination of Tc.

end of each cooling/heating cycle. The Tc values were determined as the intersection points between the steepest tangent to a v(T) curve and the linear extension of the high-temperature section of the curve. Fig. 1 presents the experimental isobars of the magnetic susceptibility measured in the stability range of x-Ti, and Fig. 2 summarizes the experimental data in the form of the Tc(P) dependence. The Tc(P) data obtained for x-Ti are also compared in Fig. 2 with similar data for x-Zr [2,3,5­7] and x-Hf [8]. All Tc(P) dependences show a rather linear behavior in the experimental interval. A linear fit through all x-Zr data gives a slope of dTc/dP = 0.115 ± 0.01 K/GPa and Tc(P = 0) = 0.54 ± 0.2 K, which agrees with the earlier estimates [2,5]. Linear extrapolation of the x-Hf and x-Ti data with the slopes of dTc/dP 0.16 K/GPa [8] and 0.07 K/GPa, respectively, results in an intersection with the P axis at

P 26.0 and 9.4 GPa. This correlates with the non-superconductive low-temperature behavior of x-Ti earlier observed [3]. We note that x-Zr and x-Hf have approximately linear Tc(P) dependences through the whole ranges of their existence up to the x­b transition. Assuming that the Tc(P) dependence for x-Ti is also linear up to the transition to the orthorhombic c-phase reported at about 128 GPa [10,11], the x-Ti superconducting temperature can increase before the transition to as high value as Tc(128) = 8.7 K. So, all Group IVb metals have low or zero temperatures of the superconducting transition both in a- and in x-phases at normal pressure, but the Tc values considerably increase when pressure is applied. This behavior can be qualitatively explained on the basis of the changes in the electronic structures. It has been determined from the calorimetric measurements on many d-metals and alloys [12] that low Tc values are correlated with low electron densities of states at the Fermi level, NF. Band-structure calculations show that applied pressure induces the s­d electron transfer in the Group IVb metals, and the estimated rate of the transfer is around 0.002 electrons/atom per GPa for a-Ti [13]. A slight increase of the d-band occupation was calculated for all Zr phases under pressure [14]. This was concomitant with the NF increase calculated for x-Zr at P 48 GPa compared to that at zero pressure [14]. Similarly, calculation of the pressure effect on the properties of the equiatomic TiV and ZrNb alloys [15] resulted in the d-band occupancy increasing at a rate of 0.003­ 0.004 electrons/atom per GPa and a nearly linear increase in Tc(P). Another mechanism for the pressure-induced Tc increase can also be assumed that involves the enhanced electron­phonon coupling due to the low-frequency anomalies in the phonon spectra. This mechanism has been suggested recently to explain the anomalous Tc(P) behavior of bcc Nb [16]. However, these kind calculations for the Group IVb metals are not available so far. Acknowledgements

(arb. un.)

6 5 4



-

Zr Zr Zr Zr Zr Hf Ti

[2] [3] [5] [6] [7] [8] - present

-Hf

This work was supported by the RFBR Grant No. 0302-17005 and by the RAS program ``The matter investigation under extreme conditions''.
-Zr -Ti

Tc (K)

3 2 1 0

References
[1] E.Yu. Tonkov, E.G. Ponyatovsky, Phase Transformations of Elements under High Pressure, CRC Press, Boca Raton, FL, 2005. [2] B. Tittman, D. Hamilton, A. Jayaraman, J. Appl. Phys. 35 (1963) 732. [3] V.F. Degtyareva, Yu.S. Karimov, A.G. Rabinkin, Fiz. Tverd. Tela 15 (1973) 3436. [4] H. Xia, G. Parthasarathy, H. Luo, Y.K. Vohra, A.L. Ruoff, Phys. Rev. B 42 (1990) 6736. [5] A. Eichler, W. Gey, Z. Physik 251 (1972) 321. [6] Y. Akahama, M. Kobayashi, H. Kawamura, J. Phys. Soc. Jpn. 59 (1990) 3843. [7] I.O. Bashkin, V.G. Tissen, M.V. Nefedova, A. Schiwek, W.B. Holzapfel, E.G. Ponyatovsky, JETP Lett. 73 (2001) 75.

0

10

20

30

40

50

60

P (GPa)
Fig. 2. Pressure effect on the superconducting transition temperatures in Ti (black squares), Zr [2,3,5­7] and Hf [8]. Solid and dotted lines are linear fits through the experimental points and their extrapolation within the x-phase ranges.


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I.O. Bashkin et al. / Physica C 453 (2007) 12­14 [12] F.J. Morin, J.P. Maita, Phys. Rev. 129 (1963) 1115. [13] J.S. Gyanchandani, S.C. Gupta, S.K. Sikka, R. Chidambaram, J. Phys.: Condensed Matter 14 (1990) 301. [14] R. Ahuja, J.M. Wills, B. Johansson, O. Eriksson, Phys. Rev. B 48 (1993) 16269. [15] P. Selvamani, G. Vaitheeswaran, V. Kanchana, M. Rajagopalan, Physica C 370 (2002) 108. [16] M. Wierzbowska, S. Gironcoli, P. Giannozzi, Available from: .

[8] I.O. Bashkin, M.V. Nefedova, V.G. Tissen, E.G. Ponyatovsky, JETP Lett. 80 (2004) 655. [9] H.K. Mao, P.M. Bell, J.W. Shaner, D.J. Steinberg, J. Appl. Phys. 49 (1978) 3276. [10] Y.K. Vohra, P.T. Spencer, Phys. Rev. Lett. 86 (2001) 3068. [11] Y. Akahama, H. Kawamura, T. LeBihan, Phys. Rev. Lett. 87 (2001) 275503; Y. Akahama, H. Kawamura, T. LeBihan, J. Phys.: Condensed Matter 14 (2002) 10583.